FOTD -- September 11, 2006 (Rating 6) Fractal visionaries and enthusiasts: A bit of four-dimensional trickery is displayed in today's image, which tries desperately to be a Julia set of East Valley but never quite makes it. If the imaginary p1 parameter had been 90, we would have had a Julia set. As it is, we have a slice rotated a mere 0.2 degree toward the Elliptic direction, but that tiny rotation makes a world of difference. The basic outer shape of an East Valley Julia set is obvious, and the goofy eyes and noses are well represented, but don't search for elephants. None are there. They have been stretched out of existence, with only their infinitely stretched remains being visible as the vertical stripes inside the outer shell. It is curious how a rotation of only 0.2 degree can make such a large difference in the appearance of Julia sets, while such a rotation makes no difference at all in most Mandelbrot images. It would seem to indicate that the Mandelbrot-shaped parts of the Julibrot are in the form of a nest of four-dimensional hyper- cylinders, with the Julia direction lying parallel to the length of the hypercylinders. As to what such a nest of 4-D hyper- cylinders might look like, I have not the slightest idea. I have seen the Fractint evolver feature mentioned recently on the list. Yes, I do use it. It is one of the most useful features of the program. About one image in three is found with the evolver. But I usually round the evolver's parameters to one or two places before calculating the final image, thereby avoiding such awkward things as an angle of 37.7394877345823114 degrees, which I would enter as 37.74 degrees. BTW, today's image was not found with the evolver. If it had been, I might have let the evolver's (p1) parameters, which determine the angle, remain unrounded. The values are quite critical. Today's image deserves its rating of a 6. In fact a rating of 6-1/2 might have been a better choice. It's a relatively inter- esting if not particularly artistic picture. The name "Elephant Trickery" refers to the tricks the image plays with the Julia set of the central point. Changing the imag(p1) parameter to 90 will reveal the true Julia set, which really is a rather interes- ting one. The calculation time of 12 minutes is true on my tired, worn-out old clunker of a computer. But as long as it boots up DOS when I turn it on, that old warhorse will continue to be my fractal machine. More modern computers are far better on the internet, but some of them go into a panic when a DOS program is loaded. Those fractalists with such sensitive machines may download the finished GIF image of today's fractal from the FOTD web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html A few more clouds and lower temperatures made Sunday less than perfect here at New Fractal Central, but the fractal cats don't mind the outside weather, since all they are permitted to do is watch it from their window. In my department, I am barely managing to keep the rush under control. So far it's going according to plan. I'll put the odds at 67 percent that the next FOTD will appear on schedule in 24 or so hours. Until that glorious time arrives, take care and check your world view for hidden errors. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Elephant_Trickery { ; time=0:12:05.35--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=0/0/0.9026217 params=90/89.8/2\ /0/0/0/0.27/0.00593 float=y maxiter=150000 inside=0 symmetry=none periodicity=10 colors=000AMX9NX8OW7PW6QV6RVBSYFS_JSaNScRSeVSgZTib\ UkfXmj_okf_lnKms5on6ph7qb7rY8sV9tS9qSEoQImQMkSQhTU\ fUYdWabXe`YiZXgYWfXWeWVdVVcTUbSTaRT`QS_PSZQR_RR_SR\ _SR`RfZdmarscqtdqtdqtdptepteouemuflufkufiughuggvgy\ vgxvhwvhuvhtwiswiqwipwjjwjhwjbxkaxkVxkUxkMxlIylGyl\ FymDymCymByn9zn8zn7zo5zo4zo3zo5xk7wh9udBtaDrZFqVGo\ SInPKlLMkIOiFQhBSf8Te5kMdUd7Vd8Vc9WcAWcBXbCYbDYaEZ\ aFZaG_`H_`I`_Ja_Ka_LbZMbZNcYOcYPdYReXSeXTfWUfWVgWW\ hVXhVYiUZiU_jU`jTakTblSclSdmSemRfnRgVtLTTgUShUShVS\ hVShWShWShXShXShYShYShZShZSh_Sh_Sh`Sh`ShaShaShbShb\ ShcShcShdRhdRheRheRhfRhfRhgRhgRhhRhhRhiRhiRhjRhjRh\ kRhkRhlRklRnmRqmRtnRwDLzFMzGMzIMzJMzLNzMNzNNzPNzQN\ zSOzTOzUOzWOzXPzZPz_Pz`PzbPzcQzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzYmz_mzamzcmzfmzhmzjmzlmzTmzUmzVmz\ WmzXmzXmzYmzZmz_mz`mz`mzamzbmzcmzcmzdmzemzfmzgmzgm\ zVmzRmzMmzImzEmzDmzCmzBmz } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| = 36 } END PARAMETER FILE=========================================